Is there any way of working out the coordinates at D? AD and BD are perpendicular and in the plane ABC.

[Matt J]

No, there is no unique solution without further conditions, e.g., or something along those lines.

[David Goodmanson]

Hi Alex,

is the intent that lines AD and BD are perpendicular?

[Alex Cooke]

Yes that’s right. Will amend the question to make it clearer. Thanks

[Matt J]

But you still haven't addressed my point about the missing condition. Are AD and BD supposed to be equal in length?

[Alex Cooke]

AD and BD are not necessarily equal in length

Answer 1

[Matt J]

Is there any way of working out the coordinates at D? ... AD and BD are not necessarily equal in length

Without a condition on the relative lengths of AD and BD, there is no unique solution for D. The infinite solution set consists of all points D lying on the circle in the plane ABC whose diameter is the chord AB.